In cut-off die sets of the double cut or pre-notching type, a notching blade is reciprocated across the upper periphery of the tubing after the tubing is clamped within the die set clamping jaws and just prior to descent of the main cut-off blade or guillotine. The pre-notching eliminates the cusping or dimpling of the tubing to a large extend to the point that subsequent reshaping of the ends of the severed length of tubing is not normally required. Whereas this general arrangement of a pre-notching cut followed by a final severing operation is generally satisfactory in producing tubing which does not require any subsequent reshaping, it is imperative that the notching blade be mounted in such a way that its reciprocating notching movement is precise and firmly supported throughout the movement of the blade.